The current Leftist-Islamist coalition wrecking much of the first world with its combination of inside-outside warfare in America, Europe, Israel, Australia and across the world seems paradoxical in nature, but has both its origins and precedents.
But what allows this Gruesome Twosome to overcome their differences is that both see a common enemy in Western Civilization. The presence of a common enemy allows the "The Enemy of my Enemy" doctrine to kick in, which is what has made many of the unlikely and self-destructive ideological relationships in history kick off. Accordingly the left has embraced Islamists as "protected minorities", more "brown people" being persecuted by the "Patriarchal Military Industrial Complex" that bedevils their nightmares. And the Islamists have learned to talk like progressives, turning out Koranic edicts about beheading your wife that sound like liberal platforms.
This is all a little like what happens when you buy a dog and a cat, that learn to get along through a little twist of species recognition, so that the dog comes to think of the cat as another dog, and the cat comes to think of the dog as another cat. But ideologically pair bondings like these don't tend to come with a happy ending.
Take Russia and Germany. During WW1, the German government sent Lenin to Russia in a sealed train in order to spread revolution and take Russia out of the war. This temporary alliance between the Monarchist Capitalists of Germany and the Bolshevik leader helped create Communism in Russia.
In turn Stalin helped wipe out German Communists paving the way for Hitler's takeover. Thus Soviet Communists helped bring Nazi Germany into being.
Both the Kaiser and Stalin were acting in their own short term interests and in doing so helped kickstart a new ideology that would ultimately nearly destroy them both. Much as the left is doing with Islam today.
Germany's express delivery of Lenin to Russia achieved their short term goals. Lenin took over. Russia signed a humiliating peace in the short term. In the longer term, Communism became a real threat to Germany itself and allowed the creation of a new Russian Empire under the red banner of a revolutionary ideology. The Communist Revolution would wind up bringing Germany to near civil war.
Meanwhile Stalin's desire for a Nazi Germany that would draw Western Europe into a war, giving him a free hand to expand Russia's borders by conquering Eastern Europe... rebounded when the Nazi monster he had helped to create wound up rampaging deep into Russian territory.
Thus Communist Russia and Nazi Germany had a hand in creating one another, and in nearly destroying one another. They should have also served as object lessons for the left in what happens when you back an ideology without thinking the long term consequences through.
Nor was this the only example. The French Monarchy backed the American revolution, only to have it rebound in a domestic revolution that toppled the French Monarchy itself. The Pope helped bankroll the Glorious Revolution that led to the House of Orange. And closer to the Islamist home, Vienna was nearly lost to the Turks because Louis XIV put his short term political interests ahead of the welfare of the rest of Europe.
The alliance between the Islamists and the Left had somewhat more legitimate roots in the Soviet Union's localization of Marxism in the Third World, and its cultivation of alliances with Arab nationalists. (This allowed the USSR to invade Afghanistan without a word of criticism from any of the Arab Muslim states.) The Soviets organized and trained a new generation of Arab terrorists, both politically and militarily. But after decades of failure in which the left nevertheless championed the USSR's Arab terrorist allies, Arab Nationalism declined and was increasingly displaced by Islamism.
Paradoxically it was the USSR's own invasion of Afghanistan that kicked the process into high gear, along with the support that the Carter Administration (now reborn as the Obama Administration) lent to Iran and the Mujahadeen in Afghanistan. Naturally the result blew up in everyone's faces. The Ayatollahs quickly demonstrated their contempt and enmity toward America. The Mujahadeen proved willing to turn on the US after they were done with the USSR.
However neither Russia nor America learned very much from the process. Russia continues to arm the Muslim world and its terrorists, and America continues to cultivate them. But the left which once strenuously opposed Islamism, has quickly come to embrace it. Just as liberals now champions Iran, despite its brutal suppression of its own liberals. And they're doing it for the same reason that Germany helped pave the way for a Communist dictatorship in Russia, and the USSR helped pave the way for a Nazi dictatorship in Germany. It seems to be in their short term political interest.
To the left, Muslims have become the ultimate oppressed minority, admired for their willingness to kill their Western "capitalist oppressors". The political and military chaos spread by Muslim terrorism has allowed the left to gain its victories, most notably in Spain, Israel and now America. This has always been a fundamental doctrine for the left, ever since Lenin's days, to transform military warfare into class warfare... or more currently into racial warfare.
And while the left employs Muslims and Muslim Terrorism as political leverage to gain power in America and Israel, and imports large numbers of Muslim immigrants into Europe to secure political victories at the polls... Islamists see the left as once again a convenient way to pave their path to power. It is doubtful that the Islamic Republic of Iran would have existed had the left not joined forces with Ayatollah Khomeni. A similar situation too is now unfolding in Egypt. And in Europe. And given time in America as well.
An ideology like Communism, Nazism or Islamism is a tiger trapped in a box. Freeing it may be in your short term interest, but it is in your long term interest to hammer the lid shut, because once the tiger is out of the box, he's just as likely to make a meal of you.